# Formula:DLMF:25.11:E18

${\displaystyle{\displaystyle{\displaystyle\HurwitzZeta^{\prime}@{0}{a}=\ln% \Gamma\left(a\right)-\tfrac{1}{2}\ln\left(2\pi\right)}}}$

## Constraint(s)

${\displaystyle{\displaystyle{\displaystyle a>0}}}$

## Note(s)

primes on ${\displaystyle{\displaystyle{\displaystyle\zeta}}}$ denote derivatives with respect to ${\displaystyle{\displaystyle{\displaystyle s}}}$

## Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

## Symbols List

: Hurwitz zeta function : http://dlmf.nist.gov/25.11#E1
: principal branch of logarithm function : http://dlmf.nist.gov/4.2#E2
: Euler's gamma function : http://dlmf.nist.gov/5.2#E1